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Page "Proofs of Fermat's theorem on sums of two squares" ¶ 43
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Moreover and by
Moreover, he rejects the contemporary accounts of Englishmen, casually adjudging them to be distorted by prejudice because `` the opinions of Englishmen are of no great value ''.
Moreover, tolerance by us of such practices results in serious waste and diversion of aid resources and in the long run generates anti-American sentiment of a kind peculiarly damaging to our political interest.
Moreover, the dominance in parasympathetic action ( with reciprocal inhibition of the sympathetic ) at the hypothalamic level induces, by its peripheral action, the autonomic symptoms of sleep and, by its action on the cortex, a lessening in the reactivity of the sensory and motor apparatus of the somatic nervous system.
Moreover, the nutritive value of irradiated foods apparently undergoes little, if any, change, although some of the fat-soluble vitamins are affected by sterilization doses.
Moreover, by systematically varying the operating conditions in the first stage and always using the optimal Af-stage policy for the remaining stages, we shall eventually find the optimal policy for all R stages.
Moreover, the diabetic patient who relies on cure by the quack device and therefore cuts off his insulin intake can be committing suicide.
Moreover, man may not supplant or frustrate the physical arrangements established by God, who through the law of rhythm has provided a natural method for the control of conception.
Moreover, if any coefficient is a fixed power of 2, the multiplication can be replaced by bit shifting.
Moreover they argued that some species have been created for the purpose of being sacrificed and eaten by humans, that it is normal for animals to kill and eat other animals, that agriculture, too, inevitably leads to the death of many animals, that plants are living beings as well and must still be destroyed, that we unintentionally and unknowingly destroy life forms all the time, and that a hunted animal has a fair chance to survive by killing the hunter.
Moreover, although Reverend Peters claimed that the term blue law was originally used by Puritan colonists, his work has since been found to be unreliable.
Moreover, Beavis and Butt-Head do a duet with Cher on " I Got You Babe " and a track by themselves called " Come to Butt-Head ".
Moreover, he also found a class of weak keys that can be detected and broken by the same attack with only 2 < sup > 4r + 1 </ sup > known plaintexts.
Moreover, by no means are all mutual managers incompetent, and conversions allows the bank to expand more easily and to grant executive stock options that are valuable to skilled managers ".
Moreover, expansion of these nations often occurred by conquest of neighbouring tribes or nations.
Moreover, during the mid-1970s the magazine was run by a Maoist editorial collective.
Moreover, these parts are explicitly determined by the respective source-densities ( see above ) and circulation densities ( see the article Curl ):
Moreover, it will be subjected to another layer of interpretation and subjectivity when read and learned by others.
Moreover, attempting to reduce one problem, say adverse selection by mandating insurance, may add to another, say moral hazard.
Moreover, any canonical ellipse can be obtained by scaling the unit circle of, defined by the equation
Moreover, the distinction between the subjective mental act, namely the content of a concept, and the ( external ) object, was developed independently by Brentano and his school, and may have surfaced as early as Brentano's 1870's lectures on logic.
Moreover to have been singled out by Aristophanes for so much comic attention is proof of popular interest in his work.
Moreover, the export logic used can be checked statically by the compiler, which allows earlier detection of scope violating calls at compile-time rather than run-time.

Moreover and theorem
Moreover, the Banach fixed point theorem states that every contraction mapping on a nonempty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.
Moreover, if the relation '≥' in the above expression is actually an equality, then and hence ; the definition of z then establishes a relation of linear dependence between u and v. This establishes the theorem.
Moreover, Gödel's second incompleteness theorem shows that the consistency of sufficiently strong effective theories of arithmetic can be tested in a particular way.
Moreover, by the envelope theorem the optimal value of a Lagrange multiplier has an interpretation as the marginal effect of the corresponding constraint constant upon the optimal attainable value of the original objective function: if we denote values at the optimum with an asterisk, then it can be shown that
Moreover, the sum of all the positive Lyapunov exponents gives an estimate of the Kolmogorov – Sinai entropy accordingly to Pesin's theorem.
Moreover Mazur's torsion theorem restricts the structure of the torsion subgroup.
Moreover, the power and authority of geometry's theorem and proof structure greatly influenced non-geometric treatises, Isaac Newton's Principia Mathematica, for example.
Moreover, one gets generalizations of the Lefschetz fixed point theorem, with terms coming from fixed point submanifolds of the group G.
Moreover the first cohomology group H < sup > 1 </ sup >( X, j < sub >*</ sub > G < sub > m, K </ sub >) is isomorphic to the Galois cohomology group H < sup > 1 </ sup >( K, K < sup >*</ sup >) which vanishes by Hilbert's theorem 90.
Moreover, all known NP proofs for this problem exhibit the prime factorization of m. This indicates that adding interaction to the proving process, may decrease the amount of knowledge that must be communicated in order to prove a theorem.
Moreover, any positive functional on this space has this form, as follows from the Riesz representation theorem.
Moreover, by the central limit theorem we have that
Moreover, the Green – Tao theorem says that for any k there exists a pair of a and b with the property that is prime for any n from 0 to k − 1.
Moreover, by Plancherel's theorem, one has
Moreover, the action allows for the easy identification of conserved quantities through Noether's theorem by studying symmetries of the action.
* Moreover, any classical theorem that is true for all standard numbers is necessarily true for all natural numbers.
Moreover, if the diameter is equal to π /√ k, then the manifold is isometric to a sphere of a constant sectional curvature k. This rigidity result is due to, and is often known as Cheng's theorem.
Moreover, the sphere ( for instance ) is spectrally rigid, by Cheng's eigenvalue comparison theorem.
Moreover, as an easy consequence of the compactness theorem, a class of σ-structures is basic elementary if and only if it is elementary and its complement is also elementary.
Moreover, the converse of Ptolemy's theorem is also true:
Moreover, θ satisfies the first set of hypotheses in Darboux's theorem, and so locally there is a coordinate chart U near p in which
Moreover, as in the case of compact simple Lie groups, the corresponding groups turned out to be almost simple as abstract groups ( Tits simplicity theorem ).
Lyndon's theorem says that if S ∪ T is unsatisfiable, then there is an interpolating sentence ρ in the language of S ∩ T that is true in all models of S and false in all models of T. Moreover, ρ has the stronger property that every relation symbol that has a positive occurrence in ρ has a positive occurrence in some formula of S and a negative occurrence in some formula of T, and every relation symbol with a negative occurrence in ρ has a negative occurrence in some formula of S and a positive occurrence in some formula of T.
Moreover, it is important for theoretical purposes, such as the Cayley – Hamilton theorem.

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